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Simplifying (2n + 6)(3n + -8) = 0 Reorder the terms: (6 + 2n)(3n + -8) = 0 Reorder the terms: (6 + 2n)(-8 + 3n) = 0 Multiply (6 + 2n) * (-8 + 3n) (6(-8 + 3n) + 2n * (-8 + 3n)) = 0 ((-8 * 6 + 3n * 6) + 2n * (-8 + 3n)) = 0 ((-48 + 18n) + 2n * (-8 + 3n)) = 0 (-48 + 18n + (-8 * 2n + 3n * 2n)) = 0 (-48 + 18n + (-16n + 6n2)) = 0 Combine like terms: 18n + -16n = 2n (-48 + 2n + 6n2) = 0 Solving -48 + 2n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + n + 3n2) = 0 Factor a trinomial. 2((-3 + -1n)(8 + -3n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667Solution
n = {-3, 2.666666667}
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